{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ornstein-Uhlenbeck process and applications\n",
    "\n",
    "\n",
    "## Contents\n",
    "   - [Ornstein-Uhlenbeck process](#sec1)\n",
    "      - [Numerical simulation](#sec1.1)\n",
    "      - [Parameters estimation from a single path](#sec1.2)\n",
    "      - [Expected time to reach the long term mean](#sec1.3)\n",
    "   - [Bond Pricing by Vasicek model](#sec2)\n",
    "   - [Tracking the OU process](#sec3)\n",
    "      - [Iterative approach for parameters estimation](#sec3.1)\n",
    "   - [Trading strategy](#sec4)\n",
    "   - [First time to exit the strip](#sec5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as scp\n",
    "import scipy.stats as ss\n",
    "from scipy.optimize import minimize\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import sparse\n",
    "from scipy.sparse.linalg import spsolve\n",
    "from mpl_toolkits import mplot3d\n",
    "from matplotlib import cm\n",
    "import scipy.special as scsp\n",
    "from scipy.integrate import quad\n",
    "from functions.Processes import OU_process\n",
    "from scipy.interpolate import RegularGridInterpolator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "# OU process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [Ornstein-Uhlenbeck process](https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process) \n",
    "is described by the following SDE: \n",
    "\n",
    "$$ dX_t = \\kappa (\\theta - X_t) dt + \\sigma dW_t .$$\n",
    "\n",
    "The parameters are:\n",
    "- $\\kappa > 0$:  mean reversion coefficient\n",
    "- $\\theta \\in \\mathbb{R}$:  long term mean  \n",
    "- $\\sigma > 0$:   volatility coefficient\n",
    "\n",
    "This process is Gaussian, Markovian and (unconditionally) stationary."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The previous SDE can be solved!  Let's do it!\n",
    "\n",
    "First of all we can define the new process $Y_t = X_t - \\theta$ such that the differential is equal $dY_t = dX_t$.      \n",
    "The SDE becomes:\n",
    "\n",
    "$$ dY_t = - \\kappa \\, Y_t \\, dt + \\sigma \\, dW_t .$$\n",
    "\n",
    "Let us introduce the function: $f(t,y) = y e^{\\kappa t}$.      \n",
    "This function has derivatives:\n",
    "\n",
    "$$ \\frac{\\partial f}{\\partial t} = y\\, \\kappa\\, e^{\\kappa t}  \\quad \\frac{\\partial f}{\\partial y} = e^{\\kappa t} \n",
    "\\quad \\frac{\\partial^2 f}{\\partial y^2} = 0 .$$\n",
    "\n",
    "We can use the Itô formula:\n",
    "\n",
    "$$ \\begin{aligned}\n",
    "d( Y_t \\, e^{\\kappa t} ) &= \\kappa \\, Y_t\\, e^{\\kappa t}\\, dt + e^{\\kappa t}\\, dY_t \\\\ \n",
    "                         &= \\kappa \\, Y_t\\, e^{\\kappa t}\\, dt + e^{\\kappa t}\\, \\biggl( - \\kappa \\, Y_t \\, dt + \\sigma \\, dW_t \\biggr) \\\\\n",
    "                         &= e^{\\kappa t} \\sigma dW_t .\n",
    "\\end{aligned} $$\n",
    "\n",
    "For convenience, let us replace the time variable $t$ with $s$, and then let us integrate both sides on $[0,t]$:\n",
    "\n",
    "$$ Y_t\\, e^{\\kappa t} - Y_0 = \\int_0^t e^{\\kappa s} \\sigma dW_t .$$\n",
    "\n",
    "At this point we can return to the original variable $X_t$ and obtain the final solution:\n",
    "\n",
    "$$ X_t = \\theta + (X_0 - \\theta)e^{-\\kappa t} + \\int_0^t \\sigma\\, e^{\\kappa (s-t)} dW_s .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moments:\n",
    "\n",
    "The **mean** of $X_t$ is:\n",
    "\n",
    "$$ \\begin{aligned}\n",
    "\\mathbb{E}[X_t] &= \\mathbb{E}\\biggl[ \\theta + (X_0 - \\theta)e^{-\\kappa t} + \\int_0^t \\sigma\\, e^{\\kappa (s-t)} dW_s \\biggr] \\\\\n",
    "                &= \\theta + (X_0 - \\theta)e^{-\\kappa t}    \n",
    "\\end{aligned}$$\n",
    "\n",
    "where the Itô integral is a martingale, $ \\mathbb{E}\\bigl[ \\int_0^t \\sigma\\, e^{\\kappa (s-t)} dW_s \\bigr] = 0$.\n",
    "\n",
    "The **covariance** is:\n",
    "\n",
    "$$ \\begin{aligned}\n",
    "\\text{Cov}[X_s, X_t] &= \\text{Cov}\\biggl[ \\int_0^s \\sigma\\, e^{\\kappa (u-s)} dW_u \\, , \\, \n",
    "\\int_0^t \\sigma\\, e^{\\kappa (v-t)} dW_v \\biggr] =  \\mathbb{E}\\biggl[ \\int_0^s \\sigma\\, e^{\\kappa (u-s)} dW_u \n",
    "\\int_0^t \\sigma\\, e^{\\kappa (v-t)} dW_v \\biggr] \\\\\n",
    "                &= \\sigma^2 e^{-\\kappa (s+t)}\\, \\mathbb{E}\\biggl[ \\int_0^s e^{\\kappa u} dW_u \n",
    "\\int_0^t e^{\\kappa v} dW_v \\biggr] \\\\\n",
    "                &= \\sigma^2 e^{-\\kappa (s+t)}\\, \\mathbb{E}\\biggl[ \\biggl( \\int_0^{\\text{min}(t,s)} e^{\\kappa u} dW_u  + \\int_{\\text{min}(t,s)}^{\\text{max}(t,s)} e^{\\kappa u} dW_u \\biggr) \\cdot \n",
    "\\int_0^{\\text{min}(t,s)} e^{\\kappa v} dW_v \\biggr] \\\\\n",
    "                &= \\sigma^2 e^{-\\kappa (s+t)}\\, \\mathbb{E}\\biggl[ \\biggl( \\int_0^{\\text{min}(t,s)} e^{\\kappa u}   dW_u \\biggr)^2 \\biggr] \\\\\n",
    "                &= \\sigma^2 e^{-\\kappa (s+t)}\\, \\int_0^{\\text{min}(t,s)} e^{2 \\kappa u} du \\; = \\; \\frac{\\sigma^2}{2\\kappa} e^{-\\kappa (s+t)}\\, \\biggl( e^{2\\kappa\\, \\text{min}(t,s)} - 1 \\biggr)  \\\\\n",
    "                &= \\frac{\\sigma^2}{2\\kappa} \\biggl( e^{-\\kappa |t-s|} - e^{-\\kappa (s+t)}\\, \\biggr),  \n",
    "\\end{aligned}$$\n",
    "\n",
    "where in the first line I remove the non-random variables, in the third line I use the independence property (expectiation of the product is equal to the product of expectation) and in the fourth line I use the Itô isometry.\n",
    "\n",
    "The **variance** is: \n",
    "\n",
    "$$ \\text{Var}[X_t] = \\text{Cov}[X_t, X_t] = \\frac{\\sigma^2}{2\\kappa} \\biggl( 1- e^{-2 \\kappa t} \\biggr).$$\n",
    "\n",
    "As $t\\to \\infty$ we obtain the **asymptotic mean**: $\\theta$ and the **asymptotic variance**: $\\frac{\\sigma^2}{2\\kappa}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.1'></a>\n",
    "## Numerical simulation\n",
    "\n",
    "We can discretize the SDE using the Euler-Maruyama numerical method (see Notebook **1.2**).\n",
    "This discretization is commented in the code below.\n",
    "\n",
    "Another possibility is to generate the dynamics from the solution of the SDE.     \n",
    "Let us consider the solution of the OU SDE obtained above. We can compute $X_{n+1}$ and consider the initial value at time $n$.\n",
    "\n",
    "$$ X_{n+1} = \\theta + (X_n - \\theta)e^{-\\kappa \\Delta t} + \\sqrt{\\frac{\\sigma^2}{2\\kappa} \\bigl( 1- e^{-2 \\kappa \\Delta t} \\bigr)} \\; \\epsilon_n $$ \n",
    "\n",
    "with $\\epsilon_n \\sim \\mathcal{N}(0,1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=42) \n",
    "\n",
    "N = 20000           # time steps \n",
    "paths = 5000        # number of paths \n",
    "T = 5\n",
    "T_vec, dt = np.linspace(0, T, N, retstep=True ) \n",
    "\n",
    "kappa = 3 \n",
    "theta = 0.5 \n",
    "sigma = 0.5     \n",
    "std_asy = np.sqrt( sigma**2 /(2*kappa) )   # asymptotic standard deviation\n",
    "\n",
    "X0 = 2\n",
    "X = np.zeros((paths,N))\n",
    "X[:,0] = X0\n",
    "W = ss.norm.rvs( loc=0, scale=1, size=(paths,N-1) )\n",
    "\n",
    "# Uncomment for Euler Maruyama\n",
    "#for t in range(0,N-1):\n",
    "#    X[:,t+1] = X[:,t] + kappa*(theta - X[:,t])*dt + sigma * np.sqrt(dt) * W[:,t]\n",
    "\n",
    "std_dt = np.sqrt( sigma**2 /(2*kappa) * (1-np.exp(-2*kappa*dt)) )\n",
    "for t in range(0,N-1):\n",
    "    X[:,t+1] = theta + np.exp(-kappa*dt)*(X[:,t]-theta) + std_dt * W[:,t]\n",
    "    \n",
    "X_T = X[:,-1]    # values of X at time T\n",
    "X_1 = X[1,:]     # a single path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean and standard deviation\n",
    "\n",
    "Since we have the possibility to generate several paths, let us consider the values at time T. We compute theoretical mean and standard deviation and compare them with the values obtained from the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical mean=0.5 and theoretical STD=0.204124\n",
      "Parameters from the fit: mean=0.499119, STD=0.200778\n"
     ]
    }
   ],
   "source": [
    "mean_T = theta + np.exp(-kappa*T) * (X0-theta) \n",
    "std_T = np.sqrt( sigma**2 /(2*kappa) * (1-np.exp(-2*kappa*T)) )\n",
    "\n",
    "param = ss.norm.fit(X_T)   # FIT from data\n",
    "print(f\"Theoretical mean={mean_T.round(6)} and theoretical STD={std_T.round(6)}\")\n",
    "print(\"Parameters from the fit: mean={0:.6f}, STD={1:.6f}\".format(*param) )  # these are MLE parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_processes = 10    # number of processes\n",
    "x = np.linspace(X_T.min(), X_T.max(), 100)\n",
    "pdf_fitted = ss.norm.pdf(x, *param)\n",
    "\n",
    "fig = plt.figure(figsize=(16,5))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(T_vec, X[:N_processes,:].T, linewidth=0.5)\n",
    "ax1.plot(T_vec, (theta + std_asy)*np.ones_like(T_vec), label=\"1 asymptotic std dev\", color=\"black\" )\n",
    "ax1.plot(T_vec, (theta - std_asy)*np.ones_like(T_vec), color=\"black\" )\n",
    "ax1.plot(T_vec, theta*np.ones_like(T_vec), label=\"Long term mean\" )\n",
    "ax1.legend(loc=\"upper right\"); ax1.set_title(f\"{N_processes} OU processes\"); ax1.set_xlabel(\"T\")\n",
    "ax2.plot(x, pdf_fitted, color='r', label=\"Normal density\")\n",
    "ax2.hist(X_T, density=True, bins=50, facecolor=\"LightBlue\", label=\"Frequency of X(T)\")\n",
    "ax2.legend(); ax2.set_title(\"Histogram vs Normal distribution\"); ax2.set_xlabel(\"X(T)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Covariance\n",
    "\n",
    "Let us also compare the theoretical covariance with the covariance obtained from the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical COV[X(t1), X(t2)] = 0.0401 with t1 = 1.4876 and t2 = 1.5001\n",
      "Computed covariance from data COV[X(t1), X(t2)] = 0.0401\n"
     ]
    }
   ],
   "source": [
    "n1 = 5950; n2 = 6000\n",
    "t1 = n1*dt; t2 = n2*dt\n",
    "\n",
    "cov_th = sigma**2 /(2*kappa) * (np.exp(-kappa*np.abs(t1-t2)) - np.exp(-kappa*(t1+t2)) )\n",
    "print(f\"Theoretical COV[X(t1), X(t2)] = {cov_th.round(4)} with t1 = {t1.round(4)} and t2 = {t2.round(4)}\")\n",
    "print(f\"Computed covariance from data COV[X(t1), X(t2)] = {np.cov( X[:,n1], X[:,n2] )[0,1].round(4)}\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.2'></a>\n",
    "## Estimation of parameters from a single path\n",
    "\n",
    "### Least squares estimation\n",
    "\n",
    "We can compute $X_{t+\\Delta t}$ and consider the initial value at time $t$.\n",
    "\n",
    "$$ \\begin{aligned}\n",
    "X_{t+\\Delta t} &= \\theta + (X_t - \\theta)e^{-\\kappa \\Delta t} + \\int_t^{t+\\Delta t} \\sigma\\, e^{\\kappa (s-t)} dW_s \\\\\n",
    "               &= \\theta \\bigl( 1-e^{-\\kappa \\Delta t} \\bigr) + e^{-\\kappa \\Delta t} X_t + \\int_t^{t+\\Delta t} \\sigma\\, e^{\\kappa (s-t)} dW_s \\\\\n",
    "               &= \\alpha + \\beta X_t + \\epsilon_t\n",
    "\\end{aligned} $$\n",
    "\n",
    "where $\\alpha = \\theta \\bigl( 1-e^{-\\kappa \\Delta t} \\bigr)$, $\\beta = e^{-\\kappa \\Delta t}$ and with $\\epsilon_t \\sim \\mathcal{N}\\biggl( 0, \\frac{\\sigma^2}{2\\kappa} \\bigl( 1- e^{-2 \\kappa \\Delta t} \\bigr)\\biggr)$.\n",
    "\n",
    "So, let us use the usual OLS method to estimate $\\alpha$, $\\beta$ and $\\sigma$.\n",
    "Then, we can obtain the parameters from the formulas:\n",
    "\n",
    "$$ \\kappa = - \\frac{\\log \\beta}{\\Delta t}, \\quad \\theta = \\frac{\\alpha}{1-\\beta}, \\quad \n",
    "\\sigma = \\text{Std}[\\epsilon_t] \\sqrt{ \\frac{2\\kappa}{1-\\beta^2} }$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS theta =  0.4027321509389097\n",
      "OLS kappa =  3.444822186777598\n",
      "OLS sigma =  0.49904604497283017\n"
     ]
    }
   ],
   "source": [
    "XX = X_1[:-1]\n",
    "YY = X_1[1:]\n",
    "beta, alpha, _, _, _ = ss.linregress(XX, YY)   # OLS\n",
    "kappa_ols = - np.log(beta)/dt\n",
    "theta_ols = alpha/(1-beta)\n",
    "res = YY - beta * XX - alpha                   # residuals\n",
    "std_resid = np.std(res, ddof=2)\n",
    "sig_ols = std_resid * np.sqrt(2*kappa_ols/(1-beta**2))\n",
    "\n",
    "print(\"OLS theta = \", theta_ols)\n",
    "print(\"OLS kappa = \", kappa_ols)\n",
    "print(\"OLS sigma = \", sig_ols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimate of the parameters doesn't look very accurate. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum Likelihood Estimation\n",
    "\n",
    "We know that \n",
    "$$ X_{i+1} \\sim \\mathcal{N}\\biggl( \\theta \\bigl( 1-e^{-\\kappa \\Delta t} \\bigr) + e^{-\\kappa \\Delta t} X_i \\, , \\, \\frac{\\sigma^2}{2\\kappa} \\bigl( 1- e^{-2 \\kappa \\Delta t} \\bigr)\\biggr)$$\n",
    "\n",
    "Let us define $\\hat \\theta^2 := \\frac{\\sigma^2}{2\\kappa} \\bigl( 1- e^{-2 \\kappa \\Delta t} \\bigr)$.\n",
    "\n",
    "At this point it is possible to write the log-likelihood function and impose the condition that first order derivatives are equal to zero. All these steps are done in [1]. \n",
    "Here I just recall the final formulas:\n",
    "\n",
    "$$ S_x = \\sum_{i=1}^n X_{i-1} \\quad S_y = \\sum_{i=1}^n X_{i} \\quad S_{xx} = \\sum_{i=1}^n X_{i-1}^2 \n",
    "\\quad S_{xy} = \\sum_{i=1}^n X_{i-1}X_{i} \\quad S_{yy} = \\sum_{i=1}^n X_{i}^2$$\n",
    "\n",
    "The parameters are:\n",
    "\n",
    "$$ \\theta = \\frac{S_y S_{xx} - S_x S_{xy}}{n(S_{xx}-S_{xy}) - (S_{x}^2 - S_{x} S_{y})} $$\n",
    "\n",
    "$$ \\kappa = - \\frac{1}{\\Delta t} \\log \\frac{S_{xy} - \\theta S_{x} - \\theta S_{y} +n\\theta^2}{S_{xx} - 2\\theta S_{x} +n \\theta^2} $$\n",
    "\n",
    "$$ \n",
    "\\hat \\theta^2 = \\frac{1}{n} \\biggl[ S_{yy} -2e^{-\\kappa \\Delta t} S_{xy} \n",
    "+ e^{-2 \\kappa \\Delta t} S{xx} -2\\theta(1-e^{- \\kappa \\Delta t})(S_y - e^{- \\kappa \\Delta t}S_x) \n",
    "+n \\theta^2(1-e^{- \\kappa \\Delta t})^2 \\biggr] $$\n",
    "$$ \\theta^2 = \\hat \\theta^2 \\frac{2\\kappa}{1-e^{-2 \\kappa \\Delta t}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sx = np.sum(XX)\n",
    "Sy = np.sum(YY)\n",
    "Sxx = XX @ XX\n",
    "Sxy = XX @ YY\n",
    "Syy = YY @ YY\n",
    "\n",
    "theta_mle = (Sy*Sxx - Sx*Sxy) / (N*(Sxx-Sxy) - (Sx**2 - Sx*Sy) )\n",
    "kappa_mle = -1/dt * np.log( (Sxy - theta_mle*Sx - theta_mle*Sy +N*theta_mle**2) \n",
    "                          / (Sxx - 2*theta_mle*Sx + N*theta_mle**2)  )\n",
    "sigma2_hat = ( Syy -2*np.exp(-kappa_mle*dt)*Sxy + np.exp(-2*kappa_mle*dt)*Sxx - 2*theta_mle*\n",
    "             (1-np.exp(-kappa_mle*dt))*(Sy-np.exp(-kappa_mle*dt)*Sx) + N*theta_mle**2 * \n",
    "              (1-np.exp(-kappa_mle*dt))**2 )/N\n",
    "sigma_mle = np.sqrt(sigma2_hat * 2*kappa_mle / (1-np.exp(-2*kappa_mle*dt)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta MLE =  0.4027057610190399\n",
      "kappa MLE =  3.4444961212451592\n",
      "sigma MLE =  0.49900861888663856\n"
     ]
    }
   ],
   "source": [
    "print(\"theta MLE = \", theta_mle)\n",
    "print(\"kappa MLE = \", kappa_mle)\n",
    "print(\"sigma MLE = \", sigma_mle)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the MLE we obtain parameters quite similar to those obtained by OLS."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1.3'></a>\n",
    "## Expected time to reach the long term mean\n",
    "\n",
    "Computation of the first hitting time density of an Ornstein-Uhlenbeck process is a long standing problem, which still remains open.       \n",
    "As explained in the introduction of the paper [5], the first hitting time of an OU process has many applications in applied mathematics, especially in mathematical finance and for the design of trading strategies.\n",
    "\n",
    "Let us define the first hitting time for the OU process:\n",
    "\n",
    "$$ T_{A,C} = \\inf\\biggl\\{ t\\geq 0 \\;: \\; X_t = A \\bigg| X_0 = C   \\biggr\\} $$\n",
    "\n",
    "Here I follow the presentation of the article [4], where the author considers the standardized problem with $\\theta=0$, $\\kappa=1$ and $\\sigma^2=2$. \n",
    "\n",
    "$$ dX_t = - X_t dt + \\sqrt{2} dW_t .$$\n",
    "\n",
    "This is a common choice, and many articles cited in [4] follow this approach (see [6]). In [5] the authors use $\\sigma=1$, (which in my opinion looks better). \n",
    "\n",
    "The standardized form can be obtained with the following change of variables:\n",
    "\n",
    "$$ \\bar t = \\kappa t, \\quad \\bar X_t = \\frac{\\sqrt{2\\kappa}}{\\sigma}(X_t-\\theta), \\quad \\bar C = \\frac{\\sqrt{2\\kappa}}{\\sigma}(C-\\theta), \\quad \\bar A = \\frac{\\sqrt{2\\kappa}}{\\sigma}(A-\\theta) $$\n",
    "\n",
    "(the bar is then removed for brevity).    \n",
    "\n",
    "Let $f_{A,C}(t)$ denote the density function of $T_{A,C}$. For $A=0$, the density has a nice expression:\n",
    "\n",
    "$$ f_{0,C}(t) = \\sqrt{\\frac{2}{\\pi}} \\frac{|C| e^{-t}}{(1-e^{-2t})^{3/2}} \\exp\\biggl[- \\frac{C^2e^{-2t}}{2(1-e^{-2t})}  \\biggr] $$\n",
    "\n",
    "Thanks to the change of variable, the expected time it takes for a process starting at $X_0$ to reach \n",
    "$\\theta$, is equal to the (scaled) expected time it takes for a process to reach $0$ starting at $\\bar C$ (set $A=\\theta$ implies $\\bar A = 0$).\n",
    "\n",
    "#### Let us estimate the expected time numerically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "T_to_theta = np.argmax(X<=theta if (X0>theta) else X>=theta, axis=1)*dt      # first passage time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expected time from X0 to theta is: 0.8894928746437323 with std error: 0.005239225702876141\n",
      "The standard deviation of the first time the process touches theta is:  0.37043215349429953\n"
     ]
    }
   ],
   "source": [
    "print(f\"The expected time from X0 to theta is: {T_to_theta.mean()} with std error: {ss.sem(T_to_theta)}\" )\n",
    "print(\"The standard deviation of the first time the process touches theta is: \", T_to_theta.std() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Now we can define the density and the new starting point C.\n",
    "\n",
    "When comparing with the histogram, we need to take into account of the time scale: $\\kappa t$.     \n",
    "Therefore the density becomes:  $\\kappa f_{0,C}(\\kappa t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def density_T_to_theta(t, C):\n",
    "    return np.sqrt(2/np.pi) * np.abs(C)*np.exp(-t) \\\n",
    "            / (1-np.exp(-2*t))**(3/2) * np.exp(-( (C**2)*np.exp(-2*t)) / (2*(1-np.exp(-2*t))) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = (X0 - theta)*np.sqrt(2*kappa)/sigma     # new starting point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,4))\n",
    "x = np.linspace(T_to_theta.min(), T_to_theta.max(), 100)\n",
    "plt.plot(x, kappa*density_T_to_theta(kappa*x,C), color=\"red\", label=\"OU hitting time density\" )\n",
    "plt.hist(T_to_theta, density=True, bins=100, facecolor=\"LightBlue\", label=\"frequencies of T\")\n",
    "plt.title(\"First passage time distribution from X0 to theta\"); plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now compute the theoretical mean and standard deviation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical expected hitting time:  0.8795633378038916\n",
      "Theoretical standard deviation of the hitting time:  0.3675713561470198\n"
     ]
    }
   ],
   "source": [
    "theoretical_T = quad( lambda t : t*kappa*density_T_to_theta(kappa*t,C), 0, 1000)[0]\n",
    "theoretical_std = np.sqrt(quad( lambda t : (t-theoretical_T)**2 *kappa*density_T_to_theta(kappa*t,C), 0,1000)[0])\n",
    "print(\"Theoretical expected hitting time: \", theoretical_T)\n",
    "print(\"Theoretical standard deviation of the hitting time: \", theoretical_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "# Bond Pricing by Vasicek model\n",
    "\n",
    "The [Vasicek model](https://en.wikipedia.org/wiki/Vasicek_model) describes the evolution of the interest rate process $\\{r_t\\}_{t \\in [0,T]}$ assuming it follows an OU process under the risk neutral dynamics (I indicate with $\\mathbb{Q}$ the risk neutral measure).\n",
    "\n",
    "We write:\n",
    "\n",
    "$$ dr_t = \\kappa (\\theta - r_t) dt + \\sigma dW_t^{\\mathbb{Q}} .$$\n",
    "\n",
    "The price of a **zero-coupon bond** has the following formula:\n",
    "\n",
    "$$ P(t,T) = \\mathbb{E}^{\\mathbb{Q}}\\biggl[ e^{\\int_t^T r_s \\, ds} \\; \\bigg|\\; \\mathcal{F}_t \\biggr]. $$\n",
    "\n",
    "Thanks to the [Feynman-Kac](https://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula) formula, we know that the previous expression is a solution of the following PDE:\n",
    "\n",
    "$$ \\frac{\\partial  P(t,r)}{\\partial t}  \n",
    "          + \\kappa (\\theta - r) \\frac{\\partial P(t,r)}{\\partial r}\n",
    "          + \\frac{1}{2} \\sigma^2 \\frac{\\partial^2  P(t,r)}{\\partial r^2} - r  P(t,r)  = 0. $$\n",
    "          \n",
    "with terminal conditions:\n",
    "\n",
    "$$ P(T,r) = 1. $$\n",
    "\n",
    "Following [2] (page 59), we can find the closed formula for the bond price under the Vasicek model:\n",
    "\n",
    "$$ P(t,T) = A(t,T) e^{-B(t,T) r_t} $$\n",
    "\n",
    "with \n",
    "\n",
    "$$ A(t,T) = exp\\biggl[ \\biggl(\\theta - \\frac{\\sigma^2}{2\\kappa^2}\\biggr)(B(t,T)-T+t) - \\frac{\\sigma^2}{4\\kappa} B(t,T)^2 \\biggr] \\quad \\text{and} \\quad \n",
    "B(t,T) = \\frac{1}{\\kappa} \\biggl( 1 - e^{-\\kappa (T-t)} \\biggr) .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Closed formula:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vasicek bond price:  0.05299806665958418\n"
     ]
    }
   ],
   "source": [
    "B = 1/kappa * ( 1-np.exp(-kappa*T) )\n",
    "A = np.exp( (theta - sigma**2/(2*kappa**2) ) * (B-T) - sigma**2/(4*kappa) * B**2  )\n",
    "P = A * np.exp(-B * X0)\n",
    "print(\"Vasicek bond price: \", P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vasicek bond price by MC: 0.05334774031341052 with std error: 0.0002745991722043543\n"
     ]
    }
   ],
   "source": [
    "disc_factor = np.exp(- X.mean(axis=1)*T )\n",
    "P_MC = np.mean( disc_factor )\n",
    "st_err = ss.sem( disc_factor )\n",
    "print(f\"Vasicek bond price by MC: {P_MC} with std error: {st_err}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### PDE\n",
    "\n",
    "As done in the notebook **2.2**, we can discretize the PDE\n",
    "using the [Upwind scheme](https://en.wikipedia.org/wiki/Upwind_scheme):    \n",
    "\n",
    "$$\n",
    " \\frac{P^{n+1}_{i} -P^{n}_{i}}{\\Delta t}  \n",
    "          + \\max \\biggl( \\kappa(\\theta-r_i),\\, 0 \\biggr) \\frac{P^{n}_{i+1} -P^{n}_{i}}{ \\Delta r} \n",
    "          + \\min \\biggl( \\kappa(\\theta-r_i),\\, 0 \\biggr) \\frac{P^{n}_{i} -P^{n}_{i-1}}{ \\Delta r} \n",
    "          + \\frac{1}{2} \\sigma^2  \\frac{P^{n}_{i+1} + P^{n}_{i-1} - 2 P^{n}_{i}}{\\Delta r^2} \n",
    "          - r_i  P^{n}_i  = 0. \n",
    "$$\n",
    "\n",
    "For convenience, let's call $\\text{max}_i = \\max \\bigl( \\kappa(\\theta-r_i),\\, 0 \\bigr)$ and $\\text{min}_i = \\min \\bigl( \\kappa(\\theta-r_i),\\, 0 \\bigr)$.     \n",
    "We can rewrite the equation above as:\n",
    "\n",
    "$$ \\begin{aligned}\n",
    "P^{n+1}_{i} =& \\; P^{n}_{i-1} \\biggl( \\text{min}_i \\frac{\\Delta t}{\\Delta r} -\\frac{1}{2} \\sigma^2 \n",
    "\\frac{\\Delta t}{\\Delta r^2} \\biggr)  \\\\\n",
    "             & + P^{n}_{i} \\biggl( 1 + r_i \\Delta t + \\frac{\\Delta t}{\\Delta r}( \\text{max}_i - \\text{min}_i ) + \\sigma^2 \\frac{\\Delta t}{\\Delta r^2} \\biggr) \\\\\n",
    "             & + P^{n}_{i+1} \\biggl( -\\text{max}_i \\frac{\\Delta t}{\\Delta r} -\\frac{1}{2} \\sigma^2 \n",
    "\\frac{\\Delta t}{\\Delta r^2} \\biggr)\n",
    "\\end{aligned}$$\n",
    "\n",
    "and, given $P^{n+1}$, we solve for $P^{n}$.     \n",
    "I also introduce the artificial lateral boundary conditions:\n",
    "\n",
    "$$ P(t, r_{\\text{min}}) = e^{-r_{\\text{min}} (T-t)} \\quad \\text{and} \\quad P(t, r_{\\text{max}}) = e^{-r_{\\text{max}} (T-t)}. $$\n",
    "\n",
    "although the resulting values are too extreme. (a high-resolution grid mitigates this problem).    \n",
    "\n",
    "See also notebook **2.1** for the description of the application of the finite difference implicit scheme. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Vasicek Bond price by PDE is:  0.05303018916704414\n"
     ]
    }
   ],
   "source": [
    "Nspace = 6000   # M space steps\n",
    "Ntime = 6000    # N time steps   \n",
    "r_max = 3            # A2\n",
    "r_min = -0.8         # A1\n",
    "r, dr = np.linspace(r_min, r_max, Nspace, retstep=True)    # space discretization\n",
    "T_array, Dt = np.linspace(0, T, Ntime, retstep=True)       # time discretization\n",
    "Payoff = 1                                                 # Bond payoff\n",
    "\n",
    "V = np.zeros((Nspace,Ntime))       # grid initialization\n",
    "offset = np.zeros(Nspace-2)        # vector to be used for the boundary terms   \n",
    "V[:,-1] = Payoff                   # terminal conditions \n",
    "V[-1,:] = np.exp(- r[-1] * (T-T_array) )    # lateral boundary condition\n",
    "V[0,:] = np.exp(- r[0] * (T-T_array) )      # lateral boundary condition\n",
    "\n",
    "# construction of the tri-diagonal matrix D\n",
    "sig2 = sigma*sigma; drr = dr * dr\n",
    "max_part = np.maximum( kappa * (theta-r[1:-1]) , 0 )        # upwind positive part\n",
    "min_part = np.minimum( kappa * (theta-r[1:-1]) , 0 )        # upwind negative part\n",
    "    \n",
    "a = min_part * (Dt/dr)  - 0.5 * (Dt/drr) * sig2 \n",
    "b = 1 + Dt*r[1:-1] + (Dt/drr)*sig2 + Dt/dr*(max_part - min_part)\n",
    "c = -max_part * (Dt/dr) - 0.5 * (Dt/drr) * sig2 \n",
    "    \n",
    "a0 = a[0]; cM = c[-1]     # boundary terms\n",
    "aa = a[1:]; cc = c[:-1]   # upper and lower diagonals \n",
    "D = sparse.diags([aa, b, cc], [-1, 0, 1], shape=(Nspace-2, Nspace-2)).tocsc()     # matrix D\n",
    "\n",
    "for n in range(Ntime-2,-1,-1):    \n",
    "    # backward computation\n",
    "    offset[0] = a0 * V[0,n]\n",
    "    offset[-1] = cM * V[-1,n]; \n",
    "    V[1:-1,n] = spsolve( D, (V[1:-1,n+1] - offset) )   \n",
    "\n",
    "# finds the bond price with initial value X0\n",
    "Price = np.interp(X0, r, V[:,0])\n",
    "print(\"The Vasicek Bond price by PDE is: \", Price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,4))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122, projection='3d')\n",
    "\n",
    "ax1.text(X0, 0.06, \"Bond Price\")\n",
    "ax1.plot([X0, X0], [0, Price], 'k--'); ax1.plot([-0.5, X0], [Price, Price], 'k--')\n",
    "ax1.plot(r, V[:,0], color='red',label=\"Barrier curve\")\n",
    "ax1.set_xlim(-0.4,2.5); ax1.set_ylim(0.025,0.12)\n",
    "ax1.set_xlabel(\"r\"); ax1.set_ylabel(\"P\"); ax1.legend(loc='upper right')\n",
    "ax1.set_title(\"Vasicek bond price at t=0\")\n",
    "\n",
    "X_plt, Y_plt = np.meshgrid(T_array, r[700:-200])  # I consider [700:-200] to remove lateral boundary effects\n",
    "ax2.plot_surface(Y_plt, X_plt, V[700:-200])\n",
    "ax2.set_title(\"Vasicek bond price surface\"); ax2.set_xlabel(\"r\"); ax2.set_ylabel(\"time\"); ax2.set_zlabel(\"V\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "# Tracking the OU process\n",
    "\n",
    "In this section I consider a **state space model** with a state process $\\{X_t, 0\\leq t \\leq T\\}$ following an OU process and an observation (or measurement) process $\\{Y_t, 0\\leq t \\leq T\\}$. \n",
    "\n",
    "In order to estimate the true state process, I will make use of the **Kalman filter**. I have alread presented the topic in the notebook **5.1** and showed its applications in the notebooks **5.2** and **5.3**.\n",
    "\n",
    "In order to create an observation process, let's add some noise to the true state process we have simulated at the beginning of the book.      "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "sig_eta = std_resid; var_eta = sig_eta**2        # error of the true state process\n",
    "sig_eps = 0.1; var_eps = sig_eps**2              # error of the measurement  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=42) \n",
    "eps = ss.norm.rvs( loc=0, scale=sig_eps, size=N )     # additional gaussian noise\n",
    "eps[0] = 0\n",
    "Y_1 = X_1 + eps             # process + noise = measurement process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot true process vs measurement process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(13,4))\n",
    "plt.plot(T_vec, X_1, linewidth=0.5, alpha=3, label=\"True process\", color=\"#1f77b4\")\n",
    "plt.plot(T_vec, theta*np.ones_like(T_vec), label=\"Long term mean\", color=\"#d62728\" )\n",
    "plt.plot(T_vec, Y_1, linewidth=0.3, alpha=0.5, label=\"Measurement process = true + noise\", color=\"#1f77b4\")\n",
    "plt.legend(); plt.title(\"OU process plus some noise\"); plt.xlabel(\"time\"); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian linear state space model:\n",
    "\n",
    "**State equation:**\n",
    "\n",
    "$$ x_k = \\alpha + \\beta x_{k-1} + \\eta_k \\quad \\text{with} \\quad \\eta_{k} \\sim \\mathcal{N}(0,\\sigma_{\\eta}^2). $$\n",
    "\n",
    "**Measurment equation:**\n",
    "\n",
    "$$ y_k= \\; x_k + \\epsilon_k \\quad \\text{with} \\quad \\epsilon_k \\sim \\mathcal{N}\\bigg(0,\\sigma_{\\epsilon}^2 \\bigg).$$\n",
    "\n",
    "### Kalman filter:\n",
    "\n",
    "Let us identify the Kalman filter elements. You can find them in the notebook **5.1** or in the [wiki page](https://en.wikipedia.org/wiki/Kalman_filter#Details).\n",
    "In order to get $F_k$, we need to rewrite the state equation as\n",
    "\n",
    "$$\n",
    "\\biggl(\\begin{array}{c}  1 \\\\ x_k \\end{array} \\biggr) = \n",
    "\\biggl(\\begin{array}{cc} 1 & 0\\\\ \\alpha & \\beta \\end{array}\\biggr)\n",
    "\\biggl(\\begin{array}{c}  1 \\\\ x_{k-1} \\end{array}\\biggr) +\n",
    "\\biggl(\\begin{array}{c} 0\\\\ \\eta_k \\end{array}\\biggr) \\quad \\text{with}  \\quad\n",
    "\\eta_k \\sim \\mathcal{N}(0, \\sigma^2_{\\eta}) $$\n",
    "\n",
    "such that $F_k = \\biggl(\\begin{array}{cc} 1 & 0\\\\ \\alpha & \\beta \\end{array}\\biggr) $\n",
    "and then ignore the first line. The matrix $ H_k=1$.    \n",
    "\n",
    "##### Predict step:\n",
    "$$ \\hat x_{k \\mid k-1} = \\alpha + \\beta \\, \\hat x_{k-1 \\mid k-1} \\quad \\quad \\text{and} \\quad \\quad  P_{k \\mid k-1} = \\beta^2 \\, P_{k-1 \\mid k-1} + \\sigma_{\\eta}^2. $$\n",
    "\n",
    "##### Auxiliary variables:\n",
    "$$ \n",
    "\\begin{aligned}\n",
    "\\tilde r_k &= y_k - \\hat x_{k \\mid k-1} &\\quad \\quad \\text{(pre-fit residual)} \\\\\n",
    "S_k &= P_{k \\mid k-1} + \\sigma_{\\epsilon}^2 &\\quad \\quad \\text{(conditional innovation covariance)} \\\\\n",
    "K_k &= \\frac{P_{k \\mid k-1}}{S_k} &\\quad \\quad \\text{(Kalman Gain)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "##### Update step:\n",
    "$$ \\hat x_{k \\mid k} = \\hat x_{k \\mid k-1} + K_k \\, \\tilde r_k  \\quad \\text{and} \\quad \n",
    "P_{k \\mid k} = P_{k \\mid k-1} \\biggl( 1- K_k \\biggr)\n",
    "$$\n",
    "\n",
    "##### Log-likelihood:\n",
    "    \n",
    "The log-likelihood function is:\n",
    "\n",
    "$$ \\log L \\big( \\alpha,\\beta, \\sigma_{\\eta}, \\sigma_{\\epsilon} \\mid y_k, y_{k-1}, ..., y_1, y_0 \\big) = -\\frac{1}{2} \n",
    "\\sum_{k=1}^N \\biggl( \\log 2\\pi + \\log S_k + \\frac{\\tilde r_k^2}{S_k}  \\biggr)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Kalman(Y, x0, P0, alpha, beta, var_eta, var_eps ):\n",
    "    \"\"\" Kalman filter algorithm for the OU process. \"\"\"\n",
    "    \n",
    "    N = len(Y)                      # length of measurements                       \n",
    "    xs = np.zeros_like(Y)           # Initialization\n",
    "    Ps = np.zeros_like(Y)\n",
    "        \n",
    "    x = x0; P = P0                        # initial values of h and P\n",
    "    log_2pi = np.log(2 * np.pi); loglikelihood = 0      # initialize log-likelihood\n",
    "    \n",
    "    for k in range(N):\n",
    "        # Prediction step\n",
    "        x_p = alpha + beta * x       # predicted h\n",
    "        P_p = beta**2 * P + var_eta  # predicted P\n",
    "\n",
    "        # auxiliary variables\n",
    "        r = Y[k] - x_p                 # residual\n",
    "        S = P_p + var_eps\n",
    "        KG = P_p / S                   # Kalman Gain\n",
    "        \n",
    "        # Update step\n",
    "        x = x_p + KG * r\n",
    "        P = P_p * (1 - KG)\n",
    "\n",
    "        loglikelihood += -0.5 * ( log_2pi + np.log(S) + (r**2/S) )      \n",
    "        xs[k] = x; Ps[k] = P\n",
    "        \n",
    "    return xs, Ps, loglikelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Train and test split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "skip_data = 1000\n",
    "training_size = 5000\n",
    "train = Y_1[skip_data:skip_data+training_size]\n",
    "test = Y_1[skip_data+training_size:]\n",
    "\n",
    "## Initial guess for teh parameters\n",
    "guess_beta, guess_alpha, _, _, _ = ss.linregress(train[1:], train[:-1])\n",
    "guess_var_eps = np.var(train[:-1] - guess_beta * train[1:] - guess_alpha, ddof=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MLE estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      fun: -4220.805792624154\n",
      " hess_inv: <4x4 LbfgsInvHessProduct with dtype=float64>\n",
      "      jac: array([0.00227374, 0.00272848, 0.00136424, 0.00190994])\n",
      "  message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n",
      "     nfev: 265\n",
      "      nit: 34\n",
      "     njev: 53\n",
      "   status: 0\n",
      "  success: True\n",
      "        x: array([3.80842172e-04, 9.99104066e-01, 5.73528205e-05, 1.00264004e-02])\n"
     ]
    }
   ],
   "source": [
    "def minus_likelihood(c):\n",
    "    \"\"\" Returns the negative log-likelihood \"\"\"\n",
    "    _, _, loglik = Kalman(train, X0, 10, c[0], c[1], c[2], c[3])\n",
    "    return -loglik\n",
    "        \n",
    "result = minimize(minus_likelihood, x0=[guess_alpha, guess_beta, 0.01, guess_var_eps], \n",
    "                      method='L-BFGS-B', bounds=[[-1,1],[1e-15,1],[1e-15,1], [1e-15,1]], tol=1e-12)\n",
    "kalman_params = result.x\n",
    "alpha_KF = kalman_params[0]\n",
    "beta_KF = kalman_params[1]\n",
    "var_eta_KF = kalman_params[2]\n",
    "var_eps_KF = kalman_params[3]\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimated parameters are very good! \n",
    "Below we can see the error of the estimation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error in estimation of alpha = 9.85%\n",
      "Error in estimation of beta = 0.0035%\n",
      "Error in estimation of var eta = 7.81%\n",
      "Error in estimation of var eps = 0.26%\n"
     ]
    }
   ],
   "source": [
    "print(f\"Error in estimation of alpha = {(np.abs(alpha-alpha_KF)/alpha *100).round(2)}%\")\n",
    "print(f\"Error in estimation of beta = {(np.abs(beta-beta_KF)/beta *100).round(4)}%\" )\n",
    "print(f\"Error in estimation of var eta = {(np.abs(var_eta-var_eta_KF)/var_eta *100).round(2)}%\")\n",
    "print(f\"Error in estimation of var eps = {(np.abs(var_eps-var_eps_KF)/var_eps *100).round(2)}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Kalman smoother\n",
    "\n",
    "Let's implement the [RTS](https://en.wikipedia.org/wiki/Kalman_filter#Rauch%E2%80%93Tung%E2%80%93Striebel) smoother.\n",
    "\n",
    "In addition to the smooth state and variance process, here I also estimate the smooth covariance $P_{k-1,k \\mid N}$ (called `Cs_smooth` in the code).\n",
    "\n",
    "$$ \\hat x_{k\\mid N} = \\mathbb{E}\\biggl[x_k \\bigg| y_N,...,y_0\\biggr] \\quad \\text{and} \\quad \n",
    "P_{k-1,k \\mid N} = \\mathbb{E}\\biggl[ \\bigl(x_k-\\hat x_{k\\mid N}\\bigr) \\bigl(x_{k-1}-\\hat x_{k-1\\mid N}\\bigr) \\,\\bigg |  \\, y_N,...,y_0\\biggr] $$\n",
    "\n",
    "The formulas to obtain $P_{k-1,k \\mid N}$ are long and can be found in [3] or in the Appendix of [7].     \n",
    "Here I just write the python code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Smoother(Y, x0, P0, alpha, beta, var_eta, var_eps):\n",
    "    \"\"\" Kalman smoother \"\"\"\n",
    "    \n",
    "    xs, Ps, _ = Kalman(Y, x0, P0, alpha, beta, var_eta, var_eps ) \n",
    "    \n",
    "    xs_smooth = np.zeros_like(xs)\n",
    "    Ps_smooth = np.zeros_like(Ps)\n",
    "    Cs_smooth = np.zeros_like(Ps)\n",
    "    C = np.zeros_like(Ps)\n",
    "    xs_smooth[-1] = xs[-1] \n",
    "    Ps_smooth[-1] = Ps[-1]\n",
    "    K = (beta**2 * Ps[-2] + var_eta) / (beta**2 * Ps[-2] + var_eta + var_eps)\n",
    "    Cs_smooth[-1] = Ps[-1] \n",
    "    Cs_smooth[-2] = beta * (1-K) * Ps[-2]\n",
    "    \n",
    "    for k in range( len(xs)-2,-1,-1):\n",
    "        C[k] = beta * Ps[k] / (beta**2 * Ps[k] + var_eta)  \n",
    "        xs_smooth[k] = xs[k] + C[k]*( xs_smooth[k+1] - (alpha + xs[k]*beta) )\n",
    "        Ps_smooth[k] = Ps[k] + C[k]**2 *( Ps_smooth[k+1] - (beta**2 * Ps[k] + var_eta) )\n",
    "        if (k == (len(xs)-2)):\n",
    "            continue\n",
    "        Cs_smooth[k] = C[k]*Ps[k+1] + C[k]*C[k+1]*( Cs_smooth[k+1]-beta*Ps[k+1] )  # covariance x(k) and x(k+1)\n",
    "    return xs_smooth, Ps_smooth, Cs_smooth "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_tmp, P_tmp, _ = Kalman(train, 1, 10, alpha_KF, beta_KF, var_eta_KF, var_eps_KF)  # to get initial values for KF\n",
    "xs, Ps, _ = Kalman(test, x_tmp[-1], P_tmp[-1], alpha_KF, beta_KF, var_eta_KF, var_eps_KF)\n",
    "x_smooth, P_smooth, _ = Smoother(test, x_tmp[-1], P_tmp[-1], alpha_KF, beta_KF, var_eta_KF, var_eps_KF)\n",
    "V_up = xs + np.sqrt(Ps)       # error up bound \n",
    "V_down = xs - np.sqrt(Ps)     # error down bound    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,5))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "ax1.plot(T_vec[skip_data+training_size:], xs, linewidth=0.5, alpha=3, label=\"Optimal state estimate\", \n",
    "                                             color=\"#1f77b4\")\n",
    "ax1.plot(T_vec[skip_data+training_size:], theta*np.ones_like(xs), label=\"Long term mean\", color=\"#d62728\")\n",
    "ax1.plot(T_vec[skip_data+training_size:], Y_1[skip_data+training_size:], linewidth=0.6, alpha=0.5, \n",
    "                                             label=\"Process + noise\", color=\"#1f77b4\")\n",
    "ax1.plot(T_vec[skip_data+training_size:], x_smooth, linewidth=0.5, alpha=3, label=\"Smoothed state estimate\", \n",
    "                                             color=\"purple\")\n",
    "ax1.fill_between(x=T_vec[skip_data+training_size:] ,y1=V_up, y2=V_down, \n",
    "                 alpha=0.7, linewidth=2, color='seagreen', label=\"Kalman error: $\\pm$ 1 std dev \")\n",
    "ax1.legend(); ax1.set_title(\"State estimation of the OU process\"); ax1.set_xlabel(\"time\");\n",
    "ax2.plot(T_vec[skip_data+training_size:], xs, linewidth=1, alpha=3, label=\"Optimal state estimator\", \n",
    "                                             color=\"blue\")\n",
    "ax2.plot(T_vec[skip_data+training_size:], theta*np.ones_like(xs), label=\"Long term mean\", color=\"#d62728\" )\n",
    "ax2.plot(T_vec[skip_data+training_size:], Y_1[skip_data+training_size:], linewidth=0.5, alpha=0.8, \n",
    "                                             label=\"Process + noise\", color=\"#1f77b4\")\n",
    "ax2.plot(T_vec[skip_data+training_size:], x_smooth, linewidth=1, alpha=3, label=\"Smoothed state estimate\", \n",
    "                                             color=\"purple\")\n",
    "ax2.fill_between(x=T_vec[skip_data+training_size:] ,y1=V_up, y2=V_down, \n",
    "                 alpha=0.7, linewidth=2, color='seagreen', label=\"Kalman error: $\\pm$ 1 std dev \")\n",
    "ax2.set_xlim(1.89,1.9); ax2.set_ylim(0.2,0.65)\n",
    "ax2.legend(); ax2.set_title(\"Zoom\"); ax2.set_xlabel(\"time\"); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set, mean linear error Kalman:  0.021392636934609466\n",
      "Average standard deviation of the estimate:  0.02687395377018235\n",
      "Test set, MSE Kalman:  0.000719986425656291\n",
      "Test set, MSE Smoother:  0.00040624843999854184\n"
     ]
    }
   ],
   "source": [
    "print(\"Test set, mean linear error Kalman: \", np.linalg.norm( xs - X_1[skip_data+training_size:], 1)/len(xs) )\n",
    "print(\"Average standard deviation of the estimate: \", np.mean( np.sqrt(Ps) ))\n",
    "print(\"Test set, MSE Kalman: \", np.linalg.norm( xs - X_1[skip_data+training_size:], 2)**2/len(xs) )\n",
    "print(\"Test set, MSE Smoother: \", np.linalg.norm( x_smooth - X_1[skip_data+training_size:], 2)**2/len(x_smooth) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the mean linear error value, we can see that the average distance of the estimated process from the true hidden process is smaller that the average standard deviation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3.1'></a>\n",
    "## Iterative approach for parameters estimation\n",
    "\n",
    "This method is described by Shumway and Stoffer (1982) in [7] and is an off-line calculation that\n",
    "makes use of smoother estimators for the Kalman Filter.      \n",
    "The Shumway and Stoffer algorithm has been widely tested (for instance in [3]).\n",
    "\n",
    "Let's recall the formulas for this iterative algorithm (taken from [3]).     \n",
    "Let's start with an initial guess \n",
    "$(\\alpha, \\beta, \\sigma_{\\eta}^2, \\sigma_{\\epsilon}^2)$ and then compute the new parameters:\n",
    "\n",
    "$$ \\alpha = \\frac{(AC-BD)}{NA - D^2}, \\quad  \\beta = \\frac{NB-CD}{NA - D^2}, \\quad \\sigma_{\\epsilon}^2 = \\frac{1}{N+1} \\sum_{k=0}^N y_k^2 - 2 y_k \\hat x_{k\\mid N} + P_{k\\mid N} + \\hat x_{k\\mid N}^2, $$\n",
    "$$\\sigma_{\\eta}^2 = \\frac{1}{N} \\sum_{k=1}^{N} \\biggl[ P_{k \\mid N} + \\hat x_{k\\mid N}^2 + \\alpha^2 + \\beta^2 P_{k-1 \\mid N} + \\beta^2 \\hat x_{k-1\\mid N}^2 - 2 \\alpha \\hat x_{k\\mid N} + 2 \\alpha \\beta \\hat x_{k-1\\mid N} \n",
    "-2 \\beta P_{k-1,k \\mid N} -2 \\beta \\hat x_{k\\mid N} \\hat x_{k-1\\mid N} \\biggr].$$\n",
    "\n",
    "Very long formulas... where I introduced:\n",
    "\n",
    "$$ A = \\sum_{k=1}^{N} \\bigl[ P_{k-1 \\mid N} + \\hat x_{k-1\\mid N}^2 \\bigr], \\quad \n",
    "B = \\sum_{k=1}^{N} \\bigl[ P_{k-1, k \\mid N} + \\hat x_{k-1\\mid N} \\hat x_{k\\mid N} \\bigr], \\quad \n",
    "C = \\sum_{k=1}^{N} \\hat x_{k\\mid N}, \\quad\n",
    "D = \\sum_{k=1}^{N} \\hat x_{k-1 \\mid N} $$\n",
    "\n",
    "The iteration runs until the improvements (measured by relative errors) are smaller than a specified error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_max = 1000                 # number of iterations\n",
    "err = 0.001                  # error in the parameters\n",
    "NN = len(train)\n",
    "alpha_SS = guess_alpha         # initial guess\n",
    "beta_SS = guess_beta           # initial guess\n",
    "var_eps_SS = guess_var_eps     # initial guess\n",
    "var_eta_SS = 0.1               # initial guess\n",
    "x_start = 1                    # initial guess\n",
    "P_start = 10                   # initial guess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of iteration:  209\n"
     ]
    }
   ],
   "source": [
    "for i in range(N_max):\n",
    "    \n",
    "    a_old = alpha_SS; b_old = beta_SS; eta_old = var_eta_SS; eps_old = var_eps_SS \n",
    "    \n",
    "    x_sm, P_sm, C_sm = Smoother(train, x_start, P_start, alpha_SS, beta_SS, var_eta_SS, var_eps_SS)\n",
    "\n",
    "    AA = np.sum( P_sm[:-1] + x_sm[:-1]**2 )                # A\n",
    "    BB = np.sum( C_sm[:-1] + x_sm[:-1]*x_sm[1:] )          # B\n",
    "    CC = np.sum(x_sm[1:])                                  # C  \n",
    "    DD = np.sum(x_sm[:-1])                                 # D  \n",
    "\n",
    "    alpha_SS = (AA*CC-BB*DD) / (NN*AA - DD**2)\n",
    "    beta_SS = (NN*BB-CC*DD) / (NN*AA - DD**2)\n",
    "    var_eta_SS = np.sum( P_sm[1:] + x_sm[1:]**2 + alpha_SS**2 + P_sm[:-1]*beta_SS**2 \\\n",
    "                   + (x_sm[:-1]*beta_SS)**2 - 2*alpha_SS*x_sm[1:] + 2*alpha_SS*beta_SS*x_sm[:-1] \\\n",
    "                   -2*beta_SS*C_sm[:-1] - 2*beta_SS*x_sm[1:]*x_sm[:-1] ) / NN\n",
    "    var_eps_SS = np.sum( train**2 - 2*train*x_sm + P_sm + x_sm**2 ) / (NN+1)\n",
    "    \n",
    "    if ( (np.abs(a_old-alpha_SS)/a_old < err) and               # iterate until there is no improvement     \n",
    "           (np.abs(b_old-beta_SS)/b_old < err) and\n",
    "           (np.abs(eta_old-var_eta_SS)/eta_old < err) and\n",
    "           (np.abs(eps_old-var_eps_SS)/eps_old < err) ):\n",
    "        print(\"Number of iteration: \", i)\n",
    "        break\n",
    "if i == N_max-1:\n",
    "    print(\"Maximum number of iterations reached \", i+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Comparison of the estimated values with the values obtained from the true state process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of estimated alpha = 0.0003889527495165138 vs real alpha = 0.00034670318459767424\n",
      "Value of estimated beta = 0.9990889510785665 vs real beta = 0.9991391221590097\n",
      "Value of estimated var_eta = 5.9412491342299224e-05 vs real var_eta = 6.221125725286099e-05\n",
      "Value of estimated var_eps = 0.010018385724213947 vs real var_eps = 0.010000000000000002\n"
     ]
    }
   ],
   "source": [
    "print(f\"Value of estimated alpha = {alpha_SS} vs real alpha = {alpha}\")\n",
    "print(f\"Value of estimated beta = {beta_SS} vs real beta = {beta}\")\n",
    "print(f\"Value of estimated var_eta = {var_eta_SS} vs real var_eta = {var_eta}\")\n",
    "print(f\"Value of estimated var_eps = {var_eps_SS} vs real var_eps = {var_eps}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### We can see that this algorithm works very well.  \n",
    "It is a good alternative to the numerical maximization of the loglikelihood function used in the previous section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec4'></a>\n",
    "## Trading strategy \n",
    "\n",
    "Let us assume that our OU process describes the dynamics of an asset, or a portfolio of assets.      \n",
    "We can implement a trading strategy that takes advantage from the mean reversion. This strategy is better known as [pair trading](https://en.wikipedia.org/wiki/Pairs_trade) (or, more in general, statistical arbitrage).\n",
    "\n",
    "The mechanics of the strategy (taken from [8]) is the following:    \n",
    "- set two bands above and below the asymptotic mean (usually at one asymptotic standard deviation) for opening the position.\n",
    "    - buy if the lower band is crossed\n",
    "    - sell if the upper band is crossed\n",
    "- set two (smaller) bands to close the position (usually at 1/10 of the standard deviation).\n",
    "\n",
    "Now let us simulate again the process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1000              # time steps\n",
    "paths = 5000          # simulated paths \n",
    "X0 = 0                # initial position \n",
    "kappa = 10 \n",
    "theta = 0 \n",
    "sigma = 2     \n",
    "T = 1                 # terminal time \n",
    "std_asy = np.sqrt( sigma**2 /(2*kappa) )   # open position\n",
    "std_10 = std_asy/10                        # close position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=41) \n",
    "OU = OU_process(sigma=sigma, theta=theta, kappa=kappa)        # creates the OU object\n",
    "X = OU.path(X0=X0, T=T, N=N, paths=paths)                     # path simulation \n",
    "process = 0                                                   # the process for the plot  \n",
    "T_vec, dt = np.linspace(0, T, N, retstep=True) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def strategy(X, mean=0, std_open=0.5, std_close=0.05, TC=0):\n",
    "    \"\"\" Implementation of the strategy.\n",
    "        - std_open = levels for opening the position. \n",
    "        - std_close = levels for closing the position.\n",
    "        - TC = Transaction costs\n",
    "    Returns:\n",
    "        - status:  at each time says if we are long=1, short=-1 or we have no open positions = 0\n",
    "        - cash: the cumulative amount of cash gained by the strategy. \n",
    "        At terminal time if there is an open position, it is closed. \n",
    "    \"\"\"\n",
    "    status = np.zeros_like(X)\n",
    "    cash = np.zeros_like(X)\n",
    "    cash[0] = X0\n",
    "    for i,x in enumerate(X):\n",
    "        if i==0:\n",
    "            continue\n",
    "        if (status[i-1] == 1) and (x >= mean-std_close):\n",
    "            status[i] = 0\n",
    "            cash[i] += x * (1+TC)\n",
    "        elif (status[i-1] == -1) and (x <= mean+std_close):\n",
    "            status[i] = 0\n",
    "            cash[i] -= x * (1+TC)\n",
    "        elif (status[i-1] == 0) and (x >= mean+std_open):\n",
    "            status[i] = -1\n",
    "            cash[i] += x * (1+TC)\n",
    "        elif (status[i-1] == 0) and (x <= mean-std_open):\n",
    "            status[i] = 1\n",
    "            cash[i] -= x * (1+TC)\n",
    "        else:\n",
    "            status[i] = status[i-1]\n",
    "            \n",
    "    if status[-1] == 1:\n",
    "        cash[-1] += x * (1+TC)\n",
    "    if status[-1] == -1:\n",
    "        cash[-1] -= x * (1+TC)\n",
    "        \n",
    "    return status, cash.cumsum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "status, cash = strategy(X[process], mean=theta, std_open=std_asy, std_close=std_10, TC=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "PnL = []     # Profit and loss for this strategy\n",
    "for i in range(paths):\n",
    "    PnL.append( strategy(X[i], mean=theta, std_open=std_asy, std_close=std_10, TC=0)[1][-1] )\n",
    "PnL = np.array(PnL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,10))\n",
    "ax1 = fig.add_subplot(221); ax2 = fig.add_subplot(223)\n",
    "ax3 = fig.add_subplot(222); ax4 = fig.add_subplot(224)\n",
    "ax1.plot(T_vec, X[process,:].T, linewidth=0.5)\n",
    "ax1.plot(T_vec, (theta + std_asy)*np.ones_like(T_vec), label=\"open short position\", color=\"sandybrown\" )\n",
    "ax1.plot(T_vec, (theta - std_asy)*np.ones_like(T_vec), label=\"open long position\", color=\"chocolate\" )\n",
    "ax1.plot(T_vec, (theta + std_10)*np.ones_like(T_vec), label=\"close short position\", color=\"gray\" )\n",
    "ax1.plot(T_vec, (theta - std_10)*np.ones_like(T_vec), label=\"close long position\", color=\"rosybrown\" )\n",
    "ax1.plot(T_vec, theta*np.ones_like(T_vec), label=\"Long term mean\", color=\"black\" )\n",
    "ax1.legend(); ax1.set_title(f\"OU process: process {process}\"); ax1.set_xlabel(\"T\")\n",
    "\n",
    "ax2.plot(T_vec,status, linestyle=\"dashed\", color=\"grey\"  )\n",
    "ax2.set_title(\"Strategy: 1=LONG, -1=SHORT, 0=No open positions \")\n",
    "\n",
    "ax3.hist(PnL, density=True, bins=100, facecolor=\"LightBlue\", label=\"frequencies\")\n",
    "x = np.linspace(PnL.min(), PnL.max(), 100)\n",
    "ax3.plot(x, ss.norm.pdf(x, loc=PnL.mean(), scale=PnL.std()), color='r', label=\"Normal density\")\n",
    "SR = PnL.mean()/PnL.std()\n",
    "ax3.legend(); ax3.set_title(f\"PnL distribution. Sharpe ratio SR = {SR.round(2)}\")\n",
    "\n",
    "ax4.plot(T_vec,cash)\n",
    "ax4.set_title(\"Cumulative amount of cash in the portfolio\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The histogram is computed considering the $PnL$ of each generated path.    \n",
    "The obtained distribution is a multimodal distribution where each peak is roughly a multiple of the band size.\n",
    "\n",
    "From the *Cumulative amount of cash* plot, we can see that we make money when we open the position. When the position is closed, a small amount of money is lost.     \n",
    "At terminal time the position must be closed.  \n",
    "\n",
    "The **sharpe ratio** is defined as $SR = \\frac{\\mathbb{E}[PnL]}{\\text{Std}[PnL]}$. There are alternative definitions involving net returns and log-returns, however here it makes more sense to consider the $PnL$ (when the initial value is 0, returns are not defined)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec5'></a>\n",
    "## First time to exit the strip\n",
    "\n",
    "Let us assume the process at time $t=0$ is contained in the strip formed by the two asymptotic standard deviations i.e. \n",
    "\n",
    "$$\\theta - \\sqrt{\\frac{\\sigma^2}{2\\kappa}} \\leq \\, X_0 \\leq \\, \\theta + \\sqrt{\\frac{\\sigma^2}{2\\kappa}}.$$ \n",
    "\n",
    "What is the expected time to exit this strip? \n",
    "\n",
    "We can estimate the time using the **Monte Carlo** simulated data, by simply taking the average of the first times the process touches the above or below lines.      (since argmax return zero if it can find a True value, check if there are zeros and if there are, replace them with a high value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Are there paths that never exit the strip? False\n"
     ]
    }
   ],
   "source": [
    "T_to_asy = np.argmax( np.logical_or( X<= -std_asy , X>= std_asy ), axis=1)*dt  # first exit time\n",
    "print(\"Are there paths that never exit the strip?\", (T_to_asy == 0).any() ) # argmax returns 0 if it can't find"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expected time is 0.07237557557557558 with standard error 0.0008702354136411929\n"
     ]
    }
   ],
   "source": [
    "print(f\"The expected time is {T_to_asy.mean()} with standard error {ss.sem(T_to_asy)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ODE approach\n",
    "\n",
    "The expected time $U$ is the solution of the following differential equation:\n",
    "\n",
    "$$ \\kappa (\\theta - x) \\frac{dU}{dx} + \\frac{1}{2} \\sigma^2 \\frac{d^2 U}{dx^2} = -1$$\n",
    "\n",
    "with boundary conditions:\n",
    "\n",
    "$$ U(B_1) = U(B_2) = 0. $$\n",
    "\n",
    "Here I called $B_1,B_2$ the levels of the asymptiotic standard deviation. \n",
    "This formula comes from [9], Chapter 10.9.\n",
    "\n",
    "#### Discretization\n",
    "\n",
    "This is a boudary value problem, that can be solved by a finite difference method. The discretization scheme is very similatr to the scheme I used for the Vasicek PDE:\n",
    "\n",
    "$$\n",
    "          + \\max \\biggl( \\kappa(\\theta-x_i),\\, 0 \\biggr) \\frac{U_{i+1} - U_{i}}{ \\Delta x} \n",
    "          + \\min \\biggl( \\kappa(\\theta-x_i),\\, 0 \\biggr) \\frac{U_{i} - U_{i-1}}{ \\Delta x} \n",
    "          + \\frac{1}{2} \\sigma^2  \\frac{U_{i+1} + U_{i-1} - 2 U_{i}}{\\Delta x^2} \n",
    "          + 1  = 0. \n",
    "$$\n",
    "\n",
    "Again, let's call $\\text{max}_i = \\max \\bigl( \\kappa(\\theta-x_i),\\, 0 \\bigr)$ and $\\text{min}_i = \\min \\bigl( \\kappa(\\theta-x_i),\\, 0 \\bigr)$.     \n",
    "We can rewrite the equation above as:\n",
    "\n",
    "$$ \n",
    "-1 = \\; U_{i-1} \\underbrace{\\biggl( - \\frac{\\text{min}_i}{\\Delta x} + \\frac{1}{2} \n",
    "\\frac{\\sigma^2}{\\Delta x^2} \\biggr)}_{a}  \n",
    "              + U_{i} \\underbrace{\\biggl( \\frac{( \\text{min}_i - \\text{max}_i )}{\\Delta x} + \\frac{\\sigma^2}{\\Delta x^2} \\biggr) }_{b}\n",
    "              + U_{i+1} \\underbrace{\\biggl( \\frac{\\text{max}_i}{\\Delta x} + \\frac{1}{2} \n",
    "\\frac{\\sigma^2}{\\Delta x^2} \\biggr)}_{c}\n",
    "$$\n",
    "\n",
    "That in matrix form becomes \n",
    "\n",
    "$$ \\mathcal{D}\\, U = -1 $$\n",
    "\n",
    "where $\\mathcal{D}$ is the usual tridiagonal matrix.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nspace = 100000             # space steps \n",
    "x_max = theta+std_asy  \n",
    "x_min = theta-std_asy\n",
    "x, dx = np.linspace(x_min, x_max, Nspace, retstep=True)    # space discretization\n",
    "\n",
    "U = np.zeros(Nspace)                 # grid initialization\n",
    "constant_term = -np.ones(Nspace-2)   # -1  \n",
    "\n",
    "# construction of the tri-diagonal matrix D\n",
    "sig2 = sigma*sigma; dxx = dx * dx\n",
    "max_part = np.maximum( kappa * (theta-x) , 0 )        # upwind positive part\n",
    "min_part = np.minimum( kappa * (theta-x) , 0 )        # upwind negative part\n",
    "\n",
    "a = -min_part/dx  + 0.5 * sig2/dxx \n",
    "b = (min_part - max_part)/dx - sig2/dxx\n",
    "c = max_part/dx + 0.5 * sig2/dxx \n",
    "    \n",
    "aa = a[1:]; cc = c[:-1]   # upper and lower diagonals \n",
    "D = sparse.diags([aa, b, cc], [-1, 0, 1], shape=(Nspace-2, Nspace-2)).tocsc()     # matrix D   \n",
    "U[1:-1] = spsolve( D, constant_term )   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot expected time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,5))\n",
    "plt.plot(x,U, label=\"Expected time curve\")\n",
    "plt.plot([X0, X0], [0, 0.06], 'k--', label=\"starting point in the simulation\");\n",
    "plt.plot([x_max, x_max], [0, 0.06], 'g--', label=\"$B_2$\");\n",
    "plt.plot([x_min, x_min], [0, 0.06], 'g--', label=\"$B_1$\"); plt.legend(loc=\"upper right\")\n",
    "plt.xlabel(\"Starting point, X0\"); plt.title(\"Expected time to exit the strip\"); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expected time starting at X_0=0,computed by ODE is 0.05957467041328912\n"
     ]
    }
   ],
   "source": [
    "expected_t_ode = np.interp(X0, x, U)\n",
    "print(f\"The expected time starting at X_0={X0},computed by ODE is {expected_t_ode}\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of the first exit time from the strip\n",
    "\n",
    "If we call $\\tau$ the first exit time, let us indicate with $P(t',x; T) = \\mathbb{P}\\big(\\tau<T \\,|\\, X_{t'}=x \\big) = \\mathbb{E}\\big[\\mathbb{1}_{\\tau<T} \\,|\\, X_{t'}=x \\big]$ the cumulative distribution function of $\\tau$ representing the probability of $\\{X_u\\, : \\, t'\\leq u \\leq T\\}$ to exit the strip before $T$.     \n",
    "Since we are interested in the forward evolution, let us define (with abuse of notation) $t = T-t'$.     \n",
    "The distribution $P(t,x)$ is solution of the following (forward) PDE (see [9] Chapter 10.8):\n",
    "\n",
    "$$ \\frac{\\partial  P(t,x)}{\\partial t}  =\n",
    "            \\kappa (\\theta - x) \\frac{\\partial P(t,x)}{\\partial x}\n",
    "          + \\frac{1}{2} \\sigma^2 \\frac{\\partial^2  P(t,x)}{\\partial x^2}. $$\n",
    "     \n",
    "with boundary conditions:\n",
    "\n",
    "$$ P(0,x) = 0, \\quad \\quad P(t, B_1) = P(t, B_2) = 1 \\quad \\text{for each }\\quad 0 \\leq t\\leq T $$\n",
    "            \n",
    "where again $B_1, B_2$ are the upper and lower barriers.\n",
    "\n",
    "The equation is almost identical to the PDE for bond pricing we found in [Sectiton Bond](#sec2), therefore the discretization is the same. The only difference is the time that goes forward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nspace = 6000   # M space steps\n",
    "Ntime = 8000    # N time steps   \n",
    "x_max = theta+std_asy    # B2  \n",
    "x_min = theta-std_asy    # B1\n",
    "x, dx = np.linspace(x_min, x_max, Nspace, retstep=True)    # space discretization\n",
    "T_array, Dt = np.linspace(0, T, Ntime, retstep=True)       # time discretization\n",
    "Payoff = 0                                                 # payoff\n",
    "\n",
    "V = np.zeros((Nspace,Ntime))       # grid initialization\n",
    "offset = np.zeros(Nspace-2)        # vector to be used for the boundary terms   \n",
    "V[:, 0] = Payoff                   # initial condition \n",
    "V[-1,:] = 1                        # lateral boundary condition\n",
    "V[0,:] = 1                         # lateral boundary condition\n",
    "\n",
    "# construction of the tri-diagonal matrix D\n",
    "sig2 = sigma*sigma; dxx = dx * dx\n",
    "max_part = np.maximum( kappa * (theta-x[1:-1]) , 0 )        # upwind positive part\n",
    "min_part = np.minimum( kappa * (theta-x[1:-1]) , 0 )        # upwind negative part\n",
    "    \n",
    "a = min_part * (Dt/dx)  - 0.5 * (Dt/dxx) * sig2 \n",
    "b = 1 + (Dt/dxx)*sig2 + Dt/dx*(max_part - min_part)\n",
    "c = -max_part * (Dt/dx) - 0.5 * (Dt/dxx) * sig2 \n",
    "    \n",
    "a0 = a[0]; cM = c[-1]     # boundary terms\n",
    "aa = a[1:]; cc = c[:-1]   # upper and lower diagonals \n",
    "D = sparse.diags([aa, b, cc], [-1, 0, 1], shape=(Nspace-2, Nspace-2)).tocsc()     # matrix D\n",
    "\n",
    "for n in range(Ntime-1):    \n",
    "    # forward computation\n",
    "    offset[0] = a0 * V[0,n]\n",
    "    offset[-1] = cM * V[-1,n]; \n",
    "    V[1:-1,n+1] = spsolve( D, (V[1:-1,n] - offset) )   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "fn = RegularGridInterpolator( (x,T_array), V, bounds_error=False, fill_value=None)   # interpolator at X0\n",
    "Cumulative = fn( (X0,T_array) )                                 # Cumulative at x=X0\n",
    "distribution = (Cumulative[1:] - Cumulative[:-1]) /Dt           # Density"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,5))\n",
    "plt.xlabel(\"Time\"); plt.title(\"Distribution of the first exit time from the strip\")\n",
    "plt.hist(T_to_theta, density=True, bins=100, facecolor=\"LightBlue\", label=\"histogram from the MC simulation\")\n",
    "plt.plot(T_array[:-1], distribution, label=\"Density from the PDE method\")\n",
    "plt.axvline(expected_t_ode, label=\"expected time\");\n",
    "plt.xlim([0,0.4])\n",
    "plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected value from density tau=0.05957056936631631 corresponds to PDE tau=0.05957467041328912\n"
     ]
    }
   ],
   "source": [
    "exp_t_integral = distribution@T_array[:-1]*Dt    # integral of t*density(t)*dt\n",
    "print(f\"Expected value from density tau={exp_t_integral} corresponds to PDE tau={expected_t_ode}\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Thijs van den Berg, [Calibrating the Ornstein-Uhlenbeck(Vasicek) model](https://www.statisticshowto.com/wp-content/uploads/2016/01/Calibrating-the-Ornstein.pdf)\n",
    "\n",
    "[2] Brigo and Mercurio, *Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit*\n",
    "\n",
    "[3] Robert J. Elliott , John Van Der Hoek & William P. Malcolm, *Pairs trading*, Quantitative Finance, (2007)\n",
    "\n",
    "[4] Finch, S., [Ornstein–Uhlenbeck process](https://oeis.org/A249417/a249417.pdf), (2004).\n",
    "\n",
    "[5] Alexander Lipton, Vadim Kaushansky, [On the First Hitting Time Density of an\n",
    "Ornstein-Uhlenbeck Process](https://arxiv.org/pdf/1810.02390.pdf), (2018)\n",
    "\n",
    "[6] L. M. Ricciardi and S. Sato, First-passage-time density and moments of the Ornstein-Uhlenbeck process, J. Appl. Probab. 25 (1988)\n",
    "\n",
    "[7] Shumway, R.H. and Stoffer, D.S., *An approach to time series smoothing and forecasting using the EM algorithm*, Journal of Time Series, (1982)\n",
    "\n",
    "[8] Cartea, A., Jaimungal, S., and Peñalva, J., *Algorithmic and high frequency trading*. Cambridge University Press, (2015)\n",
    "\n",
    "[9] Paul Wilmott, *Paul Wilmott on quantitative finance*, (2006)"
   ]
  }
 ],
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